Semilinear hyperbolic equations (Q5892657)

The lecture notes were first presented by the author at the nonlinear hyperbolic week on Tsukuba University in 1997 (see Zbl 0959.35002). The author explains how to derive sharp a priori estimates which enable one to prove global in time existence of solutions to the semilinear wave equation and nonlinear Klein-Gordon equation by using some useful tools which include basic facts of functional analysis, interpolation theorem, Fourier transform, Sobolev spaces, pseudo-differential operators, weighted Sobolev spaces with fractional order and Fourier transform on a hyperboloid. The lecture notes are useful not only to scientific workers but also to graduate students.